Optimal synthesis of Delta-Sigma modulator topologies considering snr variation

This paper presents a method for optimal synthesis of Delta-Sigma (ΔΣ) modulator topologies in terms of statistical SNR (Signal-to-Noise Ratio) variation. A ΔΣ modulator template topology is used to represent many possible Delta-Sigma modulator topologies. Then a symbolic formulation of statistical SNR variation is systematically derived from the template topology so that variation of capacitors are directly translated to SNR variation. To facilitate the search for an optimal topology, a MINLP (Mixed-Integer Nonlinearly Constrained Programming) program is formulated. By solving the MINLP program, an optimal solution with least statistical SNR variation can be obtained. Experiments have shown the solved optimal topologies have less SNR variation compared to traditional ones.